The Indians rallied to score twice in the bottom of the eighth, forging a 3-3 tie, but the Rockies came right back in the next half-inning when Smith golfed a 2-2 pitch from Chris Perez (2-3) into the right field stands.
Matt Belisle (5-2) got the victory despite blowing a two-run lead in the eighth and Huston Street hurled a scoreless bottom of the ninth for his 22nd save.
Smith cracked a two-run homer the sixth and finished 3-for-4. Jason Giambi added three hits and a run scored for the Rockies, who clinched their three-game series with the Indians.
Travis Hafner and Travis Buck provided RBI singles to rally Cleveland in the eighth.
Notable deaths of 2014 [PHOTOS]